Based on the information given, can you determine that the quadrilateral must be a parallelogram? explain.

given xn=nz and ny=nw

Yes, you can determine the shape is a parallelogram.

Using the information that is given about the congruent sides and the fact that you have a pair of vertical angles, you can state the triangle XNY is congruent to triangle ZNW. 

Now that you know the triangles are congruent, you can set up alternate interior angles are congruent to prove that the outside lines are also parallel. This would make it a parallelogram.

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